Mn$_{2}$La$_{3}$Sb$_{3}$O$_{14}$ Structure: A3B2C14D3_hR22_166_d_ab_c2h_e-001
| Prototype | La$_{3}$Mn$_{2}$O$_{14}$Sb$_{3}$ |
| AFLOW prototype label | A3B2C14D3_hR22_166_d_ab_c2h_e-001 |
| ICSD | 191137 |
| Pearson symbol | hR22 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A3B2C14D3_hR22_166_d_ab_c2h_e-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}$ |
Other compounds with this structure
Mg$_{2}$Dy$_{3}$Sb$_{3}$O$_{14}$, Mg$_{2}$Er$_{3}$Sb$_{3}$O$_{14}$, Mg$_{2}$Gd$_{3}$Sb$_{3}$O$_{14}$, Mg$_{2}$Ho$_{3}$Sb$_{3}$O$_{14}$, Mg$_{2}$Nd$_{3}$Sb$_{3}$O$_{14}$, Mg$_{2}$Pr$_{3}$Sb$_{3}$O$_{14}$, Mg$_{2}$Tb$_{3}$Sb$_{3}$O$_{14}$, Mg$_{2}$Tm$_{3}$Sb$_{3}$O$_{14}$, Mg$_{2}$Yb$_{3}$Sb$_{3}$O$_{14}$, Mn$_{2}$Pr$_{3}$Sb$_{3}$O$_{14}$, Mn$_{2}$Nd$_{3}$Sb$_{3}$O$_{14}$, Zn$_{2}$Dy$_{3}$Sb$_{3}$O$_{14}$, Zn$_{2}$Er$_{3}$Sb$_{3}$O$_{14}$, Zn$_{2}$Gd$_{3}$Sb$_{3}$O$_{14}$, Zn$_{2}$Ho$_{3}$Sb$_{3}$O$_{14}$, Zn$_{2}$Nd$_{3}$Sb$_{3}$O$_{14}$, Zn$_{2}$Pr$_{3}$Sb$_{3}$O$_{14}$, Zn$_{2}$Tb$_{3}$Sb$_{3}$O$_{14}$, Zn$_{2}$Tm$_{3}$Sb$_{3}$O$_{14}$, Zn$_{2}$Yb$_{3}$Sb$_{3}$O$_{14}$
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Mn I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Mn II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | O I |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | O I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | La I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | La I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | La I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (3e) | Sb I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (3e) | Sb I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (3e) | Sb I |
| $\mathbf{B_{11}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{12}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{13}}$ | = | $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{14}}$ | = | $- z_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{15}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{16}}$ | = | $- x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{17}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{18}}$ | = | $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{19}}$ | = | $x_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{20}}$ | = | $- z_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{21}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{22}}$ | = | $- x_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | O III |
References
- W. T. Fu and D. J. W. Ijdo, Crystal structure of Mn$_{2}$Ln$_{3}$Sb$_{3}$O$_{14}$ (Ln=La, Pr and Nd): A new ordered rhombohedral pyrochlore, J. Solid State Chem. 213, 165–168 (2014), doi:10.1016/j.jssc.2014.02.025.
Found in
- Inorganic Crystal Structure Database. Entry 191137 (La3Mn2Sb3O14).
Prototype Generator
aflow --proto=A3B2C14D3_hR22_166_d_ab_c2h_e --params=$a,c/a,x_{3},x_{6},z_{6},x_{7},z_{7}$